2016/01/09 by A. G. Ramm, Ramm, A. G.
Engineering · Mathematics · Physics and Astronomy · #35B99 #35K20 #35Q41 #35R30 #74A30 #74G75 #80A20 #80M40 #FOS: Physical sciences #Heat Transfer and Mathematical Modeling #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Radiative Heat Transfer Studies #math-ph #math.MP #msc:35B99 #msc:35K20 #msc:35Q41 #msc:35R30 #msc:74A30 #msc:74G75 #msc:80A20 #msc:80M40
paper · pdf · doi:10.48550/arxiv.1601.02138
arXiv admin note: text overlap with arXiv:1207.0565
arxiv created 2016/01/09 · openalex publication_date 2016/01/09 · arxiv updated 2016/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting field is derived when the characteristic size a of the small bodies tends to zero, their total number N(a) tends to infinity at a suitable rate, and the distance d = d(a) between neighboring small bodies tends to zero: a << d, lima→ 0(a)/(d(a))=0. No periodicity is assumed about the distribution of the small bodies. These results are basic for a method of creating a medium in which heat signals are transmitted along a given line. The technical part for this method is based on an inverse problem of finding potential with prescribed eigenvalues.